\section{Conclusion}
Despite this paper presents many possibilities to create or accept two-dimensional languages, this shows what is generally possible with picture
languages. For example one could also present logic formulas where a picture
$p$ is seen as a grid graph with $l_1(p) * l_2(p)$ vertices which represents a
relational structure~\cite{giammarresi1996monadic}. Furthermore, it could be shown
how turing machines are operating on given input pictures or a special type of
matrix grammars that are working with a control
sequence~\cite{subramanian1985extension}. As can be seen, another topic one could take about to further extent would be one of the numerous special forms of the presented models. 

The class REC is directly derived from the one-dimensional case. Nevertheless,
its properties are different to regular string languages. The closure properties
are almost equal except for complementation. But we do not know whether a
deterministic counterpart recognizing REC exists. Furthermore, no decision-making
algorithm is as efficient as the one-dimensional ones. As far as we know, no
two-dimensional approach matches the properties of the regular string languages.

On a final note, we want to present an overview of all language families, we described in this paper:

\begin{center}
\begin{tikzpicture}
    \node (rec) at ( 0, 0) {REC}; 
    \node (ds) at (-0.7, 1) {$\familyOf{DS}$};
    \node (ws) at (-1.4, 2) {$\familyOf{WS}$};
    \node (mu-WA) at (-2.1, 3) {$\familyOf{$\mu $-WA}$};
    \node (pcfre) at (-2.8, 4) {$\familyOf{PCFRE}$};
    \node (ta) at (-3.5, 5) {$\familyOf{TA}$};
    \node (ts) at (-4.2, 6) {$\familyOf{TS}$};
    \node (loc) at (-6.3, 4.8) {LOC};
    \node (hv-loc) at (-5.7, 3.5) {$hv$-LOC};
    \node (cfre) at (-4.2, 1.9) {$\familyOf{CFRE}$};
    \node (reg) at (-6.6, 1.9) {REG};
    \node (snake-drec) at (-6.5, 0) {$Snake$-DREC};
    \node (scan-drec) at (-3, 0) {$Scan$-DREC};
    \node (urec) at(-2.0, -1.2) {UREC};
    \node (urec-union) at (-6.5, -1) {$Col$-UREC $\cup$ $Row$-UREC};
    \node (urec-inter) at (-6, -3.5) {$Col$-UREC $\cap$ $Row$-UREC};
    \node (co-rec) at (-3, -2.3) {$co$-REC};
    \node (drec) at (-1, -3) {DREC};
    \node (diag-drec) at (-4, -4.8) {$diag$-DREC};
    \node (2drta) at (-7.1, -6) {$\familyOf{2DRTA}$};
    \node (sdrec) at (-1, -4) {SDREC};
    \node (2dsa) at (0, -5) {$\familyOf{2DSA}$};
    \node (2dma1) at (2, -2) {$\familyOf{2DMA(1)}$};
    \node (2ota) at (6, -2) {$\familyOf{2OTA}$};
    \node (2nsa) at (2.5, -5) {$\familyOf{2NSA}$};
    \node (2nma1) at (3.3, -3.1) {$\familyOf{2NMA(1)}$};
    \node (2sa) at (4.7, -4.1) {$\familyOf{2SA}$};
    \node (4fa) at (1.8, -6.3) {$\familyOf{4FA}$};
    \node (4nfa) at (3.1, -7.6) {$\familyOf{4NFA}$};
    \node (4dfa) at (4.5, -8.8) {$\familyOf{4DFA}$};
    \node (2nota) at (6, -6) {$\familyOf{2NOTA}$};
    \node (2dota) at (6, -7.6) {$\familyOf{2DOTA}$};
    \node (re) at (4, -0.5) {$\familyOf{RE}$};
    \node (sfre) at (4, 0.8) {$\familyOf{SFRE}$};
    \node (si-2rta) at (3.8, 1.8) {$\familyOf{$si$-2RTA}$};
    \node (mu-dwa) at (3.5, 2.8) {$\familyOf{$\mu $-DWA}$};
    \node (mu-4dwa) at (1, 4) {$\familyOf{$\mu $-4DWA}$};
    \node (4dfa-union-dwa) at (1.2, 6) {$\familyOf{4DFA} \cup \familyOf{$\mu $-DWA}$};
    
    \node (psml) at (2.5, -13) {$\familyOf{PSML}$};
	\node (csml) at (2.5, -12) {$\familyOf{CSML}$};
	\node (cfml) at (2.5, -11) {$\familyOf{CFML}$};
	\node (rml) at (2.5, -10) {$\familyOf{RML}$};
	
	\node (ex-psml) at (5.5, -13) {$\familyOf{Ex-PSML}$}; 
	\node (ex-csml) at (5.5, -12) {$\familyOf{Ex-CSML}$};
	\node (ex-cfml) at (5.5, -11) {$\familyOf{Ex-CFML}$};
	\node (ex-rml) at (5.5, -10) {$\familyOf{Ex-RML}$};
	
	\node (tmma) at (-0.5, -13) {$\familyOf{TMMA}$};
	\node (lbma) at (-0.5, -12) {$\familyOf{LBMA}$};
	\node (pdma) at (-0.5, -11) {$\familyOf{PDMA}$};
	\node (fsma) at (-0.5, -10) {$\familyOf{FSMA}$};
	
	\node (tcsml) at (-3.5, -12) {$\familyOf{TCSML}$};
	\node (tcfml) at (-3.5, -11) {$\familyOf{TCFML}$};
	\node (trml) at (-3.5, -10) {$\familyOf{TRML}$};

	\node (rtcsml) at (-7, -12) {$\familyOf{(R)TCSML}$};
	\node (rtcfml) at (-7, -11) {$\familyOf{(R)TCFML}$};
	\node (rtrml) at (-7, -10) {$\familyOf{(R)TRML}$};
	
	\node (ial) at (4, -14.5) {$\familyOf{IAL}$};
	\node (mal) at (1, -14.5) {$\familyOf{MAL}$};
	\node (cfal) at (-2, -14.5) {$\familyOf{CFAL}$};
	\node (ral) at (-5, -14.5) {$\familyOf{RAL}$};

    \begin{scope}[every path/.style={-}]
       	\path (rec) -- (ds)  node[pos=.5,sloped] {$=$};
       	\path (ds) -- (ws)  node[pos=.5,sloped] {$=$};
       	\path (ws) -- (mu-WA)  node[pos=.5,sloped] {$=$};
       	\path (mu-WA) -- (pcfre)  node[pos=.5,sloped] {$=$};
       	\path (pcfre) -- (ta)  node[pos=.5,sloped] {$=$};
       	\path (ta) -- (ts)  node[pos=.5,sloped] {$=$};
       	\path (ts) -- (loc)  node[pos=.5,sloped] {$\subset$};
       	\path (loc) -- (hv-loc)  node[pos=.5,sloped] {$\supset$};
       	\path (hv-loc) -- (cfre)  node[pos=.5,sloped] {$\subset$};
       	\path (cfre) -- (reg)  node[pos=.5,sloped] {$\subset$};
       	\draw (cfre) -- (rec)  node[fill=white,pos=.5,sloped] {$\subset$};
       	\path (snake-drec) -- (scan-drec) node[pos=.5,sloped] {$\subset$};
       	\path (snake-drec) -- (urec-union)  node[pos=.5,sloped] {$=$};
       	\draw (urec-union) -- (urec-inter)  node[fill=white,pos=.5,sloped] {$\supset$};
       	\path (scan-drec) -- (urec)  node[pos=.5,sloped] {$\subseteq$};
       	\path (urec-union) -- (urec)  node[pos=.5,sloped] {$\subset$};
       	\path (rec) -- (urec)  node[pos=.5,sloped] {$\subset$};
       	\path (2drta) -- (diag-drec)  node[pos=.5,sloped] {$\supset$};
       	\path (urec-inter) -- (diag-drec)  node[pos=.5,sloped] {$\supset$};
       	\draw (2dsa) -- (diag-drec)  node[fill=white,pos=.5,sloped] {$\subseteq$};
       	\path (2dsa) -- (sdrec)  node[pos=.5,sloped] {$\subset$};
       	\path (drec) -- (sdrec)  node[pos=.5,sloped] {$\subseteq$};
       	\path (co-rec) -- (drec)  node[pos=.5,sloped] {$\supseteq$};
       	\draw (rec) -- (drec)  node[fill=white,pos=.5,sloped] {$\subseteq$};
       	\draw (2dsa) -- (rec)  node[fill=white,pos=.5,sloped] {$\neq$};
       	\path (2dsa) -- (4fa)  node[pos=.5,sloped] {$\supset$};
       	\path (4fa) -- (4nfa)  node[pos=.5,sloped] {$\supset$};
       	\path (4nfa) -- (4dfa)  node[pos=.5,sloped] {$\supset$};
       	\path (4dfa) -- (2dota)  node[pos=.5,sloped] {$\neq$};
       	\draw (4nfa) -- (2nota)  node[fill=white,pos=.5,sloped] {$\subset$};
       	\path (2dota) -- (2nota)  node[pos=.5,sloped] {$\subset$};
       	\draw (2dsa) -- (2nsa)  node[fill=white,pos=.5,sloped] {$\subset$};
       	\path (2nsa) -- (2sa)  node[pos=.5,sloped] {$\subset$};
       	\draw (2sa) -- (2ota)  node[fill=white,pos=.5,sloped] {$\supseteq$};
       	\draw (2nota) -- (2ota)  node[fill=white,pos=.5,sloped] {$\subset$};
       	\draw (2nma1) -- (2nsa)  node[fill=white,pos=.5,sloped] {$\not\supset$};
       	\path (2nma1) -- (2ota)  node[pos=.5,sloped] {$\neq$};
       	\draw (rec) -- (re)  node[fill=white,pos=.5,sloped] {$\neq$};
       	\draw (rec) -- (sfre)  node[fill=white,pos=.5,sloped] {$\neq$};
       	\draw (rec) -- (si-2rta)  node[fill=white,pos=.5,sloped] {$\subset$};
       	\draw (rec) -- (mu-dwa)  node[fill=white,pos=.5,sloped] {$\supseteq$};
       	\draw (rec) -- (mu-4dwa)  node[fill=white,pos=.5,sloped] {$\supseteq$};
       	\draw (mu-4dwa) -- (4dfa-union-dwa)  node[fill=white,pos=.5,sloped] {$\supset$};
       	\draw (2dsa) -- (2dma1)  node[fill=white,pos=.5,sloped] {$\supset$};
       	\path (2dma1) -- (2ota)  node[pos=.5,sloped] {$\neq$};
       	\draw (rec) -- (2ota)  node[fill=white,pos=.5,sloped] {$=$};
       	
       	\path (ex-csml) -- (ex-psml)  node[pos=.5,sloped] {$\subset$};
		\path (ex-cfml) -- (ex-csml)  node[pos=.5,sloped] {$\subset$};
		\path (ex-rml) -- (ex-cfml)  node[pos=.5,sloped] {$\subset$};
       
		\path (csml) -- (psml)  node[pos=.5,sloped] {$\subset$};
		\path (cfml) -- (csml)  node[pos=.5,sloped] {$\subset$};
		\path (rml) -- (cfml)  node[pos=.5,sloped] {$\subset$};
		
		\path (psml) -- (ex-psml)  node[pos=.5,sloped] {$\subset$};
		\path (csml) -- (ex-csml)  node[pos=.5,sloped] {$\subset$};
		\path (cfml) -- (ex-cfml)  node[pos=.5,sloped] {$\subset$};
		\path (rml) -- (ex-rml)  node[pos=.5,sloped] {$\subset$};
		
		\path (lbma) -- (tmma)  node[pos=.5,sloped] {$\subset$};
		\path (pdma) -- (lbma)  node[pos=.5,sloped] {$\subset$};
		\path (fsma) -- (pdma)  node[pos=.5,sloped] {$\subset$};
		
		\path (tmma) -- (psml)  node[pos=.5,sloped] {$=$};
		\path (lbma) -- (csml)  node[pos=.5,sloped] {$=$};
		\path (pdma) -- (cfml)  node[pos=.5,sloped] {$=$};
		\path (fsma) -- (rml)  node[pos=.5,sloped] {$=$};
		
		\path (tcfml) -- (tcsml)  node[pos=.5,sloped] {$\subset$};
		\path (trml) -- (tcfml)  node[pos=.5,sloped] {$\subset$};
    
    		\path (lbma) -- (tcsml)  node[pos=.5,sloped] {$\supset$};
		\path (pdma) -- (tcfml)  node[pos=.5,sloped] {$\supset$};
		\path (fsma) -- (trml)  node[pos=.5,sloped] {$\supset$};
		
    		\path (rtcfml) -- (rtcsml)  node[pos=.5,sloped] {$\subset$};
		\path (rtrml) -- (rtcfml)  node[pos=.5,sloped] {$\subset$};

    		\path (rtcsml) -- (tcsml)  node[pos=.5,sloped] {$=$};
		\path (rtcfml) -- (tcfml)  node[pos=.5,sloped] {$=$};
		\path (rtrml) -- (trml)  node[pos=.5,sloped] {$=$};

		\path (mal) -- (ial)  node[pos=.5,sloped] {$\subset$};
		\path (cfal) -- (mal)  node[pos=.5,sloped] {$\subset$};
		\path (ral) -- (cfal)  node[pos=.5,sloped] {$\subset$};
		
		\draw (rml) -- (4dfa)  node[fill=white,pos=.5,sloped] {$\subset$};
    \end{scope}
\end{tikzpicture}
\end{center}